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系統識別號 U0002-0207200517551100
中文論文名稱 含界層裂紋之彈壓電複合材料之動力破壞分析
英文論文名稱 Dynamic Fracture Analysis of an Interface Crack between Purely Elastic and Piezoelectric Materials.
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 93
學期 2
出版年 94
研究生中文姓名 蔡忠翰
研究生英文姓名 Chung-Han Tsai
學號 692370678
學位類別 碩士
語文別 中文
口試日期 2005-06-16
論文頁數 206頁
口試委員 指導教授-應宜雄
委員-馬劍清
委員-劉昭華
委員-應宜雄
中文關鍵字 複合壓電材料  界面裂紋  應力強度因子  動力破壞 
英文關鍵字 piezoelectric  interface crack  stress intensity factor  dynamic fracture 
學科別分類 學科別應用科學航空太空
中文摘要 本文研究內含電極邊界彈壓電複合材料之界層裂紋的動力破壞問題,解析一含半無限長界面裂紋之彈壓電複合材料,於裂紋面上施予均佈反平面動力載荷之破壞行為,並研究於距離裂紋尖端h處之裂紋面分別為受一對反平面動力點載荷之暫態效應,本文使用積分轉換法與Wiener-Hopf技巧推導彈壓電複合材料於一次拉普拉氏轉換域中,受空間指數應力之基本解,並利用此基本解來解析此包含特徵長度的複合壓電材料動力暫態問題,接著使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的解。最後本文針對應力、電位移、應力強度因子與電位移強度因子等解析解,做詳細的數值計算與討論。
英文摘要 In this study, the transient response of a semi-infinite, interface crack between hexagonal piezoelectric and purly elastic media with the electrode boundary condition is investigated. The useful fundamental solutions are derived and the solutions can be determined by superposition of the fundamental solutions in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in Laplace transform domain) on the interface crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient Full-Field solutions to the problem with uniform loads, and exact transient solutions of intensity factors to the problem with concentrated loads are both derived. Finally, numerical results are evaluated and discussed in detail.
論文目次 目錄
目錄 ……………………………………………………………… I
圖表目錄 ………………………………………………………… V
第一章 緒論 ………………………………………………………1
1.1 研究動機 …………………………………………………1
1.2 文獻回顧 …………………………………………………3
1.3 內容簡介 …………………………………………………8
第二章 理論基礎與基本解 ………………………………………9
2.1 線彈性壓電材料之控制與本構方程式 …………………9
2.2 純彈性材料之控制與本構方程式 ……………………15
2.3 拉普拉斯轉換與Cagniard-de Hoop method …………16
2.3.1 拉普拉斯轉換 …………………………………………16
2.3.2 Cagniard-de Hoop method ……………………………17
第三章 半無窮長界面裂紋受反平面動力均佈載荷之全場解析 ……………………18
3.1 問題描述 ………………………………………………18
3.2 G(λ)函數拆解 …………………………………………24
3.3 N(λ)函數拆解 …………………………………………27
3.4 存在MT表面波之複合壓電材料之理論解析 …………38
3.4.1 壓電材料剪力波波速大於純彈性材料剪力波波速之拉普拉斯域解(bbg>b(e)) ………………………38
3.4.2 壓電材料剪力波波速大於純彈性材料剪力波波速之時域解(bbg>b(e)) ………………………………43
3.4.3 壓電材料剪力波波速小於純彈性材料剪力波波速之拉普拉斯域解 ……53
3.4.4 壓電材料剪力波波速小於純彈性材料剪力波波速之時域解 ……………56
3.5 V(λ)函數拆解 …………………………………………64
3.6 J(λ)函數拆解 …………………………………………67
3.7 無MT表面波之複合壓電材料之理論解析 ……………69
3.7.1 壓電材料剪力波波速大於純彈性材料剪力波波速之拉普拉斯域解(b(e)>bbg) ………………………69
3.7.2 壓電材料剪力波波速大於純彈性材料剪力波波速之時域解(b(e)>bbg) ………………………………73
3.7.3 壓電材料剪力波波速小於純彈性材料剪力波波速之拉普拉斯域解 ……80
3.7.4 壓電材料剪力波波速小於純彈性材料剪力波波速之時域解 ……………83
3.8 數值計算與討論 ………………………………………92
第四章 半無窮長界面裂紋受反平面動力點載荷之破壞解析 ………………………97
4.1 存在MT表面波之複合壓電材料之基本解 ……………97
4.1.1 壓電材料剪力波波速大於純彈性材料剪力波波速之基本解(bbg>b(e)) …………………………………97
4.1.2 壓電材料剪力波波速小於純彈性材料剪力波波速之基本解 ……………105
4.2 無MT表面波之複合壓電材料之基本解 ………………110
4.2.1 壓電材料剪力波波速大於純彈性材料剪力波波速之基本解(b(e)>bbg) ………………………………110
4.2.2 壓電材料剪力波波速小於純彈性材料剪力波波速之基本解 ……………115
4.3 問題描述 ………………………………………………120
4.4 存在MT表面波之複合壓電材料之理論解析 …………121
4.4.1 壓電材料剪力波波速大於純彈性材料剪力波波速之應力及電位移強度因子(bbg>b(e)) ……………122
4.4.2 壓電材料剪力波波速小於純彈性材料剪力波波速之應力及電位移強度因子 …………………………129
4.5 無MT表面波之複合壓電材料之理論解析 ……………131
4.5.1 壓電材料剪力波波速大於純彈性材料剪力波波速之應力及電位移強度因子(b(e)>bbg) ……………131
4.5.2 壓電材料剪力波波速小於純彈性材料剪力波波速之應力及電位移強度因子 …………………………133
4.6 數值計算與討論 ………………………………………135
第五章 成果與討論 ……………………………………………140
5.1 本文結論 ………………………………………………140
5.2 本文成果 ………………………………………………141
5.2 尚待研究的方向 ………………………………………142
參考文獻 …………………………………………………………144


圖表目錄
表3.1 PZT4搭配不同彈性材料之根的現象 ……………………162
表3.2 PZT4搭配不同彈性材料之波速比較表 …………………163
表3.3 壓電材料常數表 …………………………………………164
表3.4 純彈性材料常數表 ………………………………………165
圖3.1 界面裂紋之問題描述 ……………………………………166
圖3.2 S1之積分路徑圖 …………………………………………167
圖3.3a c(e)>c之λ平面圖 ………………………………………168
圖3.3b c>c(e)之λ平面圖 ………………………………………169
圖3.4a c(e)>c有根形式之v平面圖 ……………………………170
圖3.4b c(e)>c無根形式之v平面圖 ……………………………170
圖3.4c c>c(e)有根形式之v平面圖 ……………………………171
圖3.4d c>c(e)有根形式之v平面圖 ……………………………171
圖3.5 S2之積分路徑圖 …………………………………………172
圖3.6 S3之積分路徑圖 …………………………………………173
圖3.7a τyz(e)逆轉換路徑圖 …………………………………174
圖3.7b τyz(e)逆轉換路徑圖 …………………………………174
圖3.8a S4之積分路徑圖 …………………………………………175
圖3.9a S5之積分路徑圖 …………………………………………176
圖3.10a PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………177
圖3.10b PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………177
圖3.11a PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………178
圖3.11b PZT4-Steel彈壓電複合材料之剪應力暫態圖 …………178
圖3.12a c>c(e)之彈壓複合材料裂紋面施加均佈載荷波前圖 …179
圖3.12b c圖3.13 30°之不同彈性材料剪應力暫態圖 ……………………180
圖3.14 60°之不同彈性材料剪應力暫態圖 ……………………181
圖3.15 90°之不同彈性材料剪應力暫態圖 ……………………182
圖3.16 120°之不同彈性材料剪應力暫態圖 ……………………183
圖3.17 150°之不同彈性材料剪應力暫態圖 ……………………184
圖3.18 -30°之不同彈性材料剪應力暫態圖 ……………………185
圖3.19 -60°之不同彈性材料剪應力暫態圖 ……………………186
圖3.20 -90°之不同彈性材料剪應力暫態圖 ……………………187
圖3.21 -120°之不同彈性材料剪應力暫態圖 …………………188
圖3.22 -150°之不同彈性材料剪應力暫態圖 …………………189
圖3.23 PZT4-Steel彈壓電複合材料之電位移暫態圖 …………190
圖3.24 30°之不同彈性材料電位移暫態圖 ……………………191
圖3.25 60°之不同彈性材料電位移暫態圖 ……………………192
圖3.26 90°之不同彈性材料電位移暫態圖 ……………………193
圖3.27 120°之不同彈性材料電位移暫態圖 ……………………194
圖3.28 150°之不同彈性材料電位移暫態圖 ……………………195
圖4.1 電極型邊界描述 …………………………………………196
圖4.2 界面裂紋之問題描述 ……………………………………197
圖4.3 Γη之積分路徑圖 ………………………………………198
圖4.4 存在MT表面波之c>c(e)積分路徑圖 ……………………199
圖4.5 函數f之積分路徑圖 ……………………………………200
圖4.6 存在MT表面波之c圖4.7 無MT表面波之c>c(e)積分路徑圖 ………………………202
圖4.8 無MT表面波之c圖4.9 受應力負載含界面裂紋之應力強度因子 ………………204
圖4.10 受應力負載含界面裂紋之電位移強度因子 ……………205
圖4.11 數值積分示意圖 …………………………………………206
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洪國彬 (2003),含預裂縫之壓電材料的力學行為,國立台灣大學應用力學研究所碩士論文。
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